%!TEX root = thesis.tex

$\mathcal{A}$-adversary.\\
$B_t$-ball around a point of radius $t$. \\
 $C$-set of codewords of error-correcting code.\\
 $\cext$-computational extractor.  See \defref{def:computational extractor}.\\
 $D$-distinguisher.\\
 $d$-length of seed in extractor.\\
 $\mathcal{D}$-class of distinguishers.\\
 $\dis$-distance function for metric space.\\
  $\ext$-randomness extractor.  See \defref{def:randomness extractor}.\\
 $\mathbb{F}$-finite field.\\
 $F$-universal hash function.\\
 GAPSVP-Gap Shortest Vector Problem.  See \cite{regevLWEsurvey}.\\
  $\gen$-generate of fuzzy extractor.  See \defref{def:fuzzy extractor}.\\
 $\Hoo$-min-entropy of random variable.\\
 $\Hav$-conditional min-entropy of random variable.\\
 $H_0$-support size of random variable.  Also known as Hartley entropy.\\
 $\tilde{H}_0$-conditional support size.  Average Hartley entropy.\\
  $H^{\hill}_{\epsilon, s}$-HILL pseudoentropy.  See \defref{def:cond hill}.\\
 $H^{\hillrlx}_{\epsilon, s}$-relaxed HILL pseudoentropy.  See \defref{def:relaxed hill}.\\
 $\Hfuzz$-fuzzy min-entropy.  See \defref{def:fuzzy min-ent}.\\
 $\hill$-shorthand for standard definition of pseudoentropy (named for \cite{DBLP:journals/siamcomp/HastadILL99}).\\
 $H^{\unprlx}_{\epsilon, s}$-relaxed unpredictability entropy.  See \defref{def:unp entropy}.\\
 $\key$-key generated by fuzzy extractor.  $\Key$ indicates random variable.\\
 $K$-key for universal hash.  The random variable is $\mathcal{K}$.\\
 \LWE-The learning with errors assumption.  See \cite{regevLWEsurvey}.\\
 $\mathcal{M}$-metric space.\\
 $m$-starting entropy of source.\\
 $\tilde{m}$-residual entropy after either running fuzzy extractor or secure sketch.\\
 $n$-security parameter.  Often we consider metric spaces of size proportional to $2^n$.\\
 $\ngl$-shrinks faster than any inverse polynomial in the input or security parameter.\\
 NP-non-deterministic polynomial time.  See \cite{sipser2012introduction}.\\
 $\neigh_t$-neighborhood of a point in the metric space.  See \defref{def:neighborhood}.\\
 $P$-public info generated by fuzzy extractor.  Lowercase for a specific instance.\\
 $\poly$-polynomial size in the input parameter or security parameter.\\
 PUF-physically unclonable function.  See \cite{pappu2002physical}.\\
  $\rec$-recover for secure sketch.  See \defref{def:secure sketch}.\\
 $\rep$-reproduce of fuzzy extractor.  See \defref{def:fuzzy extractor}.\\
$\seed$-public value of randomness extractor.  Length denoted by $d$.\\
 $\mathbf{SD}$-statistical distance.\\
 SIVP-Short independent vectors problem.  See \cite{regevLWEsurvey}.\\
 $\sketch$-secure sketch.  See \defref{def:secure sketch}.\\
 $ss$-public value produced by $\sketch$.\\
 $t$-desired error tolerance.\\
 $U$-uniform distribution, often parameterized by length.\\
 $W$-source distribution.\\
 $\mathcal{W}$-family of distributions accepted to fuzzy extractor.\\
 $w$-initial reading.\\
 $w'$-subsequent noisy reading provided to fuzzy extractor. \\
 $\weight$-Hamming weight of a string.  Number of nonzero symbols.\\
 $\mathcal{Z}$-alphabet for Hamming metric.\\
$\gamma$-number of symbols for Hamming constructions.\\
 $\delta$-error of fuzzy extractor.\\
 $\epsilon$-advantage of distinguisher.\\
 $\kappa$-key length.

